Using small brush, scrub fresh or frozen truffles under cold running water. Using sharp thin knife, remove peel from truffles and reserve for sauce. Thinly shave truffles using V-slicer or truffle shaver; cover and set aside.

Pat duck breasts dry with paper towels. Cut off any sinew from breast meat. Place breasts on work surface. Using fingers or small sharp knife, pull or cut skin with fat away from meat from both long sides of duck breast almost to center, leaving 1-inch-wide strip of fat attached to meat in center (do not cut through center strip). Lift up flaps of duck skin and fat and arrange sliced truffles over breast meat under fat on each, dividing equally. Press skin flaps down over truffles to cover completely. Using sharp knife, score top of duck skin in 1/2-inch diamond pattern, being careful not to cut through fat. (Can be made 1 day ahead. Cover broth, duck, and truffle peel separately and chill.)